Adaptive filters can be used in various systems, but require powerful processors if time critical operation is needed. An example of such an application is an echo canceller in a telecommunications system.
FIG. 1 is a schematic diagram of an example prior art telecommunications system 100a in which an echo canceller 120 employs an adaptive filter. The telecommunications system 100a includes a near-end telephone 105a and a far-end telephone 105b. The near-end telephone 105a is connected to a near-end hybrid 110a via a telephone line 125a. The far-end telephone 105b is connected to a far-end hybrid 110b via a telephone line 125b. The near-end hybrid 110a is connected to the far-end hybrid 110b via telephone lines 130 and 135 that are part of a public switched telephone network (PSTN) 115. The echo canceller 120 resides in the PSTN to remove an echo signal caused by the far-end hybrid 110b as a result of hybrid mismatch.
FIG. 2 is a schematic diagram of an alternative example of the prior art telecommunications system 100b in which the near-end telephone 105a, near-end hybrid 110a, and associated telephone line 125a are replaced with a wireless subsystem 200. The wireless subsystem 200 includes a handset 205 connected to a base station 210 via a wireless link 215. The wireless subsystem 200 also includes a mobile station controller (MSC) 220 connected to the PSTN 115, having the echo canceller 120 with adaptive filter, that transmits voice signals via the telephone lines 130 and 135 to the far-end hybrid 110b. 
FIGS. 3–5 are schematic diagrams of adaptive filters used in various applications.
FIG. 3 provides details of the echo cancellation application in the prior art telecommunications systems of FIGS. 1 and 2. Referring to FIG. 3, in general, the echo canceller 120 determines and cancels echos received from an unknown system 505, where the unknown system 505 includes the set of transmission lines 130, 135 and the far-end hybrid 110b. Because of a hybrid mismatch, an echo signal 510 travels from the far-end hybrid 110b via the telephone line 135 back to the echo canceller 120.
The echo canceller 120 includes an adaptive filter 320a that uses adaptive filter parameters, wk, or weights. A summing unit 315 sums the output, yk, of the adaptive filter 320a with a far-end signal, dk, which is composed of the echo signal 510, far-end speech, and noise. The output from the summing unit 315 is an error signal, ek, which is just the far-end speech and noise if the adaptive filter 320a in the echo canceller 120 perfectly matches the echo signal 510.
FIG. 4 is an example of the adaptive filter 320a used in a prior art system identification application 300. The adaptive filter 320a is used in concert with the summing unit 315 to determine characteristics of an unknown plant 310. If the squared error, |ek|2, is minimal, then the adaptive filter 320a has reached convergence, and the characteristics of the unknown plant 310 are determined from converged parameters in the adaptive filter 320a. 
FIG. 5 is a schematic diagram of a channel equalization application 400 in which the adaptive filter 320a is used to determine characteristics of a channel 410, such as a speech channel in the PSTN 115 (FIG. 1). A delay unit 405 is used to estimate the delay of the channel 410. If the squared error, |ek|2, is minimized, then the adaptive filter 320a has reached convergence and has removed distortion the channel 410 may have added to a signal traveling in the channel 410. The characteristics of the channel 410 can be determined as a function of the adaptive filter parameters, wk, in the adaptive filter 320a. 
In channel equalization applications, slow convergence of adaptive filters can result from an existence of deep nulls in the channel frequency response. This invariably leads to a large eigenspread and a requirement for long channel equalizers in the case of baud-rate sampling. In acoustic echo cancellation applications, the echo path is estimated by an adaptive filter. The acoustic echo path often requires a large number of parameters for adequate modeling. Speech signals also present a particularly challenging case because they tend to be non-stationary and to have lowpass spectral features.